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Non-Abelian Fourier Transforms and N...

Slipper, Aaron Arthur Gordon,

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Non-Abelian Fourier Transforms and Normalized Intertwining Operators Over Finite Fields for General Parabolic Subgroups /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Non-Abelian Fourier Transforms and Normalized Intertwining Operators Over Finite Fields for General Parabolic Subgroups // Aaron Arthur Gordon Slipper.
作者:	Slipper, Aaron Arthur Gordon,
面頁冊數:	1 electronic resource (79 pages)
附註:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31240265
ISBN:	9798382783628

Non-Abelian Fourier Transforms and Normalized Intertwining Operators Over Finite Fields for General Parabolic Subgroups /
Slipper, Aaron Arthur Gordon,

Non-Abelian Fourier Transforms and Normalized Intertwining Operators Over Finite Fields for General Parabolic Subgroups /Aaron Arthur Gordon Slipper. - 1 electronic resource (79 pages)

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

Let G be a (split) reductive group over \uD835\uDD3Dq, T a maximal torus, T ' ⊂ T a subtorus, and M = ZG(T') - a reductive subgroup of G. Let P denote a parabolic subgroup of G with Levi factor M; let U = Ru(P) (resp., Uop = Ru(Pop)); let G/U (resp., G/Uop) denote the affinizations of the quasi-affine homogeneous spaces G/U (resp., G/Uop). We propose a construction for a non-abelian Fourier transform S(G/U(\uD835\uDD3Dq), ℂ) → S(G/Uop(\uD835\uDD3Dq), ℂ), where S denotes a certain restricted subspace of functions on G/U(\uD835\uDD3Dq). We conjecture that this transform is involutive (i.e., satisfies the analogue of Fourier inversion) and provide evidence for this conjecture in concrete low-rank cases. Along the way, we will prove a finite-field Fourier transform for affine quadratic cones, and construct the complete set of finite-field normalized intertwining operators for the standard Borels in SL3.

English

ISBN: 9798382783628Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Basic affine space

Non-Abelian Fourier Transforms and Normalized Intertwining Operators Over Finite Fields for General Parabolic Subgroups /
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520 $a Let G be a (split) reductive group over \uD835\uDD3Dq, T a maximal torus, T ' ⊂ T a subtorus, and M = ZG(T') - a reductive subgroup of G. Let P denote a parabolic subgroup of G with Levi factor M; let U = Ru(P) (resp., Uop = Ru(Pop)); let G/U (resp., G/Uop) denote the affinizations of the quasi-affine homogeneous spaces G/U (resp., G/Uop). We propose a construction for a non-abelian Fourier transform S(G/U(\uD835\uDD3Dq), ℂ) → S(G/Uop(\uD835\uDD3Dq), ℂ), where S denotes a certain restricted subspace of functions on G/U(\uD835\uDD3Dq). We conjecture that this transform is involutive (i.e., satisfies the analogue of Fourier inversion) and provide evidence for this conjecture in concrete low-rank cases. Along the way, we will prove a finite-field Fourier transform for affine quadratic cones, and construct the complete set of finite-field normalized intertwining operators for the standard Borels in SL3.
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590 $a School code: 0330
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Basic affine space
653 $a Fourier transform
653 $a Parabolic subgroup
653 $a Reductive monoid
653 $a Representation theory
690 $a 0405
690 $a 0642
690 $a 0364
710 2 $a The University of Chicago. $b Mathematics. $e degree granting institution. $3 3823067
720 1 $a Ngo, Bảo Chau $e degree supervisor.
720 1 $a Kato, Kazuya $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 85-12B.
790 $a 0330
791 $a Ph.D.
792 $a 2024
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